The annulus-filtered E and B modes in cosmic microwave background radiation polarization

Although it has previously been recognized that the cosmic microwave background (CMB) polarization measurement on a sky ring is able to separate the B- and E- mode patterns, we show that the rotational symmetry of the CMB polarization measurement is indeed unique, in that it enables the B and E modes to be separately measured in a simple and clean manner. The separation of the B and E modes can in principle be achieved even with a single-polarization detector of arbitrary beam pattern. Based on this premise, a specific observing strategy is suggested where the telescope scans along a sky circle with the polarimeter axis always oriented to a fixed direction with respect to the radial direction of the sky circle. The observational strategy for B-mode measurements can further be refined by choosing appropriate beam sizes to suppress the accidental E-mode leakage. We present the expected variances of the measured E- and B-mode surface brightness fluctuations as functions of the sky annulus radius and beam size. The measured peak power is expected to be up to 10% of the total power contained in the CMB polarization fluctuations for both B and E modes. The temperature-polarization, or T-E, correlation can be measured by the present method as well. By adopting this strategy, the Array for Microwave Background Anisotropy experiment is expected to detect, in a single sky annulus, a 1sigma B-mode signal in 340 hr.